Brillouin–Wigner perturbation theory
E33422
Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Brillouin–Wigner perturbation theory canonical | 2 |
| Brillouin–Wigner expansion | 1 |
| quasi-degenerate perturbation theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T248997 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Brillouin–Wigner perturbation theory Context triple: [Rayleigh–Schrödinger perturbation theory, relatedTo, Brillouin–Wigner perturbation theory]
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A.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
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B.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
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C.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
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D.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
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E.
The Nature of the Chemical Bond
The Nature of the Chemical Bond is a landmark chemistry book by Linus Pauling that systematically explains chemical bonding using quantum mechanics and became one of the most influential scientific texts of the 20th century.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Brillouin–Wigner perturbation theory Target entity description: Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
-
A.
Rayleigh–Schrödinger perturbation theory
Rayleigh–Schrödinger perturbation theory is a fundamental method in quantum mechanics for approximating the energies and states of a system by treating interactions as small corrections to an exactly solvable problem.
-
B.
Herzberg–Teller approximation
The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
-
C.
Born–Oppenheimer approximation
The Born–Oppenheimer approximation is a fundamental method in molecular quantum mechanics that simplifies calculations by treating nuclear motion as much slower than electronic motion, allowing their behaviors to be separated.
-
D.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
E.
The Nature of the Chemical Bond
The Nature of the Chemical Bond is a landmark chemistry book by Linus Pauling that systematically explains chemical bonding using quantum mechanics and became one of the most influential scientific texts of the 20th century.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
perturbation theory
ⓘ
quantum mechanical formalism ⓘ |
| advantage | can improve convergence of perturbation series in some problems ⓘ |
| aimsTo |
obtain improved approximations to eigenstates
ⓘ
obtain improved approximations to eigenvalues ⓘ |
| appliedIn | nuclear shell-model calculations ⓘ |
| appliesTo |
discrete spectra
ⓘ
time-independent Hamiltonians ⓘ |
| assumes | existence of a solvable unperturbed Hamiltonian ⓘ |
| basedOn | partition of Hamiltonian into unperturbed and perturbation parts ⓘ |
| category | approximation method in quantum theory ⓘ |
| characteristic | energy appearing on both sides of the eigenvalue equation ⓘ |
| comparedTo | Rayleigh–Schrödinger perturbation theory ⓘ |
| contrastWith | Rayleigh–Schrödinger perturbation theory using energy-independent effective Hamiltonian ⓘ |
| developedIn | 20th century ⓘ |
| feature | nonlinear dependence of energy corrections on the exact energy ⓘ |
| field | quantum mechanics ⓘ |
| focusesOn | corrections to eigenvalues and eigenvectors of the unperturbed Hamiltonian ⓘ |
| formalismType | time-independent perturbation theory ⓘ |
| framework | Hilbert space of quantum states ⓘ |
| goal | improve accuracy beyond low-order perturbation results ⓘ |
| involves | projection operators onto model space and complementary space ⓘ |
| limitation |
leads to implicit equations for energies
ⓘ
requires self-consistent solution for eigenvalues ⓘ |
| mathematicalForm | series expansion in powers of the perturbation ⓘ |
| namedAfter |
Eugene Wigner
ⓘ
Léon Brillouin ⓘ |
| relatedConcept |
Brillouin–Wigner perturbation theory
self-linksurface differs
ⓘ
surface form:
Brillouin–Wigner expansion
Brillouin–Wigner perturbation theory self-linksurface differs ⓘ
surface form:
quasi-degenerate perturbation theory
|
| relatedTo |
Feshbach projection formalism
ⓘ
effective Hamiltonian methods ⓘ |
| requires |
choice of model space
ⓘ
definition of projection operators ⓘ |
| usedFor |
bound-state problems in quantum mechanics
ⓘ
many-body quantum systems ⓘ |
| usedIn |
atomic physics
ⓘ
condensed matter physics ⓘ molecular physics ⓘ |
| usedToDerive | effective interactions in model spaces ⓘ |
| uses | energy-dependent effective Hamiltonian ⓘ |
| yields | energy-dependent effective Hamiltonian in model space ⓘ |
How these facts were elicited
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Subject: Brillouin–Wigner perturbation theory Description of subject: Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.